Question

21.2. Let f(n) and g(n) be functions from N→R. Prove or disprove the following statements. (a)...

21.2. Let f(n) and g(n) be functions from N→R. Prove or disprove the following statements.

(a) f(n) = O(g(n)) implies g(n) = O(f(n)).

(c) f(n)=?(g(n)) if and only if (n)=O(g(n)) and g(n)=O(f(n)).

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. (15 pts total) Prove or disprove each of the following claims, where f(n) and g(n)...
1. (15 pts total) Prove or disprove each of the following claims, where f(n) and g(n) are functions on positive values. (a) f(n) = O(g(n)) implies g(n) = Ω(f(n)) (b) f(n) = O(g(n)) implies 2^f(n) = O(2^g(n)) (c) f(n) = O((f(n))^2)
Prove or disprove the following: (a) Let f : A → B and g : B...
Prove or disprove the following: (a) Let f : A → B and g : B → C be two functions. If g is onto, then g ◦ f : A → C is onto. (b) Let f : A → B and g : B → C be two functions. If g is one-to-one, then g ◦ f : A → C is one-to-one. (c) There exist functions f : A → B and g : B → C...
5. Prove or disprove the following statements: (a) Let R be a relation on the set...
5. Prove or disprove the following statements: (a) Let R be a relation on the set Z of integers such that xRy if and only if xy ≥ 1. Then, R is irreflexive. (b) Let R be a relation on the set Z of integers such that xRy if and only if x = y + 1 or x = y − 1. Then, R is irreflexive. (c) Let R and S be reflexive relations on a set A. Then,...
Let f,g be positive real-valued functions. Use the definition of big-O to prove: If f(n) is...
Let f,g be positive real-valued functions. Use the definition of big-O to prove: If f(n) is O(g(n)), then f2(n)+f4(n) is O(g2(n)+g4(n)).
. Let f : Z → N be function. a. Prove or disprove: f is not...
. Let f : Z → N be function. a. Prove or disprove: f is not strictly increasing. b. Prove or disprove: f is not strictly decreasing.
1. Let A = {1,2,3,4} and let F be the set of all functions f from...
1. Let A = {1,2,3,4} and let F be the set of all functions f from A to A. Prove or disprove each of the following statements. (a)For all functions f, g, h∈F, if f◦g=f◦h then g=h. (b)For all functions f, g, h∈F, iff◦g=f◦h and f is one-to-one then g=h. (c) For all functions f, g, h ∈ F , if g ◦ f = h ◦ f then g = h. (d) For all functions f, g, h ∈...
Let N be a normal subgroup of G. Prove or disprove the following assertion: N and...
Let N be a normal subgroup of G. Prove or disprove the following assertion: N and G/N have composition series ----> G has a composition series.
Prove or disprove: If f:A→B and g:B→A are functions and g◦f is a bijection, then f...
Prove or disprove: If f:A→B and g:B→A are functions and g◦f is a bijection, then f and g are bijections.
1.Let f and g be two functions such that f(n)/g(n) converges to a positive value less...
1.Let f and g be two functions such that f(n)/g(n) converges to a positive value less than 1 as n tends to infinity. Which of the following is necessarily true? Select one: a. g(n)=Ω(f(n)) b. f(n)=Ω(g(n)) c. f(n)=O(g(n)) d. g(n)=O(f(n)) e. All of the answers 2. If T(n)=n+23 log(2n) where the base of the log is 2, then which of the following is true: Select one: a. T(n)=θ(n^2) b. T(n)=θ(n) c. T(n)=θ(n^3) d. T(n)=θ(3^n) 3. Let f and g be...
Let f and g be measurable unsigned functions on R^d . Assume f(x) ≤ g(x) for...
Let f and g be measurable unsigned functions on R^d . Assume f(x) ≤ g(x) for almost every x. Prove that the integral of f dx ≤ Integral of g dx.